Solve the System of Equations y=x-1 y=1/2x+1

$y = x - 1$ $y = \frac{1}{2} x + 1$

Step 1

Eliminate the equal sides of each equation and combine.

$x - 1 = \frac{1}{2} x + 1$

Step 2

Solve $x - 1 = \frac{1}{2} x + 1$ for $x$ .

Combine $\frac{1}{2}$ and $x$ .

$x - 1 = \frac{x}{2} + 1$

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{x}{2}$ from both sides of the equation.

$x - 1 - \frac{x}{2} = 1$

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x \cdot \frac{2}{2} - \frac{x}{2} - 1 = 1$

Combine $x$ and $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} - \frac{x}{2} - 1 = 1$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - x}{2} - 1 = 1$

Subtract $x$ from $x \cdot 2$ .

Reorder $x$ and $2$ .

$\frac{2 \cdot x - x}{2} - 1 = 1$

Subtract $x$ from $2 \cdot x$ .

$\frac{x}{2} - 1 = 1$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$\frac{x}{2} = 1 + 1$

Add $1$ and $1$ .

$\frac{x}{2} = 2$

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 2$

Rewrite the expression.

$x = 2 \cdot 2$

Simplify the right side.

Multiply $2$ by $2$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Substitute $4$ for $x$ .

$y = \frac{1}{2} \cdot (4) + 1$

Substitute $4$ for $x$ in $y = \frac{1}{2} \cdot (4) + 1$ and solve for $y$ .

Multiply $\frac{1}{2}$ by $4$ .

$y = \frac{1}{2} \cdot 4 + 1$

Simplify $\frac{1}{2} \cdot 4 + 1$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{1}{2} \cdot (2 (2)) + 1$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 2) + 1$

Rewrite the expression.

$y = 2 + 1$

Add $2$ and $1$ .

$y = 3$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 3)$

Equation Form:

$x = 4, y = 3$

Step 6

Solve the System of Equations y=x-1 y=1/2x+1

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